Control of Multipartite Entanglement through Anisotropy against Thermal Noise

Abstract

Preserving multipartite entanglement in open many-body quantum systems is fundamentally limited by unavoidable environmental noise. We study the open-system dynamics of multipartite entanglement in an anisotropic XXZ spin chain interacting with a thermal spin bath, focusing on two states with distinct types of multipartite entanglement: the generalized GHZ and the generalized W state. Using a master-equation approach combined with the Bethe ansatz technique, we show analytically that robustness of multipartite entanglement at low temperatures can be enhanced by suitably tuning the anisotropy of the system. Our results highlight interaction-induced spectral control as a mechanism for stabilizing multipartite entanglement in quantum computing platforms.

Figures (4)

• Figure 1: Schematic of an interacting one-dimensional spin chain embedded in a spin bath. The intra-chain anisotropy can be externally tuned to control the multipartite entanglement against broadband thermal fluctuations.
• Figure 2: Dynamics of the generalized GHZ state. (a,b) geometric genuine multipartite entanglement: (a) as a function of scaled time $(\lambda t)$ for different temperatures and anisotropies, and (b) as a function of temperature and anisotropy at long times $(\lambda t = 100)$. (c,d) Lower bound of the distillation fraction: (c) as a function of scaled time $(\lambda t)$ for different temperatures and anisotropies, and (d) as a function of temperature and anisotropy at long times $(\lambda t = 100)$. The plots are generated using $N/N_b \equiv f = 0.01$, effective decay rate $\gamma = 1$, and average bath spectral density $n = 10$.
• Figure 3: Dynamics of the generalized $W$ state. (a,b) Fraction of the generalized $W$ state in the classical mixture: (a) as a function of scaled time $(\lambda t)$ for different temperatures and anisotropies, and (b) as a function of temperature and anisotropy at long times $(\lambda t = 100)$. (c,d) Upper bound of the geometric collective mutipartite entanglement: (c) as a function of scaled time $(\lambda t)$ for different temperatures and anisotropies, and (d) as a function of temperature and anisotropy at long times $(\lambda t = 100)$. The plots are generated using $N/N_b \equiv f = 0.01$, effective decay rate $\gamma = 1$, and average bath spectral density $n = 10$.
• Figure 4: Zero-net-momentum energy eigenvalues of the XXZ model in the thermodynamic limit $N \to \infty$, corresponding to the zero-magnon sector, the one-magnon sector, and the two-magnon scattering and bound-state sectors. These eigenvalues are represented by black, green, blue, and red lines, respectively.